To automate the process of unsubscribing customers who request removal via email replies, the Marketing Cloud admin should first ensure that Reply Mail Management (RMM) is enabled in the account. This feature manages responses to emails sent from Marketing Cloud. Additionally, within RMM settings, the admin should select "Unsubscribe Manual requests." This setting enables the system to automatically process unsubscribe requests from customers who manually reply asking to be removed from mailing lists. This helps in maintaining compliance with customer preferences and email marketing laws.